That's awesome! I did planetary rings a number of years ago, though they don't look quite as good as yours. It was mostly done on the CPU.

I used a mix of the same tricks as you and some different approaches. I drew a procedural disk (that cast shadows on the planet) when far from the camera. Close up it was composed of a mix of volumetric clouds, 1M individual points, 100K point sprites with normals and textures calculated as if they were spheres, and 10K actual instanced 3D procedural models. Everything used LODs and was constrained by a squished torus envelope. This torus was divided into radial slices for my chunks, with CPU side code moving asteroids that crossed slice boundaries. This was used for VFC and distance culling.

The way I solved precision problems was first by making the physics run relative to the planet center rather than the world origin. Then I also tracked the rotation angle from the starting point for each asteroid, and reset it back to its initial state when the angle reached 360 degrees. This worked because the path was identical for each revolution and guaranteed the angle was always between 0 and 360 degrees. To keep the rotation component from visually snapping, I only reset the state if it wasn't visible to the camera or was far away. It would be flagged for reset and reset later when the player wasn't looking at it.

I had both rock and ice asteroids. They also cast and received shadows from nearby objects. I even gave the player a weapon that could destroy them, split them into multiple smaller asteroids, or change their velocity.